In the first half it was the visitors who came closest to breaking the deadlock, but then they were reduced in number when Conor Townsend collected two yellow cards in as many minutes and was sent off by referee Mark Brown.
The Millers started brightly and Matt Tubbs set up Kieran Agard after just two minutes but his shot whistled just wide of the post.
But after 34 minutes it took a great save by Rotherham goalkeeper Adam Collin to deny Carlisle. Matty Robson got in a great cross and Sean O’Hanlon’s powerful header looked destined for the back of the net but Collin somehow turned it away for a corner.
The Cumbrians were reduced to 10 men second before half-time. Townsend was booked for a foul on Richard Brindley and the in added time his late tackle on Tubbs earned him a second yellow and an early bath.
But despite 45 minutes of almost constant pressure, Rotherham could not find a way through the visitors’ defence – even though their goal did lead something of a charmed life.
Max Ehmer and Robson cleared off the line, Ben Amos saved from substitute Tom Eaves and Tubbs fired into the side netting, but Carlisle hung on desperately for a thoroughly deserved point.